A few years ago, Sarah Connolly's husband flew out to join her in New York, where she was singing Romeo in a run of Bellini's I Capuleti e i Montecchi. He was met at the airport by a young man who looked oddly like his wife. "I think he was a bit frightened," says Connolly. "But it was just after a show, and I hadn't had time to get the wig or anything off."

Connolly's ability to convince in opera's so-called trouser roles - women playing boys or men - has been a calling card throughout a career that now finds her arguably at the top of a glorious roster of outstanding British mezzo-sopranos. Her big break, 10 years ago, came when she was cast as Handel's petulant emperor Xerxes at English National Opera, in Nicholas Hytner's memorable staging. More recently, there has been her imperious Julius Caesar in Glyndebourne's hit Handel production, and an impetuous Octavian in Strauss's Der Rosenkavalier at Scottish Opera and ENO, both of which continued her long-standing working partnership with the director David McVicar.

Now she is dressing as Romeo again - but so far, rehearsals for Orpha Phelan's new Opera North production involve nothing more self-consciously masculine than trousers and a battered pair of plimsolls. No funny looks, then, as we repair for coffee and cake in the bookshop around the corner from Leeds's Grand theatre. "I definitely spend more time on stage being a man," Connolly says. "The roles that suit my voice and physicality work out that way." Even in those plimsolls, she is tall and strapping, not the ingénue or little- sister type, and she is not tempted by the flirtier female roles, such as Rosina in The Barber of Seville. "A conductor said to me recently that because I sing fast Handel arias, I must also sing Rossini, but I don't really care for it - I don't like decoration for the sake of it." Bellini's writing can be seen as the pinnacle of the 19th-century bel canto school, in which beauty and agility of voice was all; but, as Connolly says, "the decoration is very much connected to the music, rather than just standing there and showing off".

The Capulets and the Montagues is Bellini's take on the Romeo and Juliet story, premiered in Venice in 1830 and brought to London's Haymarket theatre three years later. Its story comes mainly via sources other than Shakespeare, but follows a similar path to the same tragic conclusion. "Bellini completely understood fragility, rejection, loyalty, the making and breaking of a promise," says Connolly. "There's something so utterly touching about the spacing in his music - the empty bars, the moments between the notes. I think he draws the character of Romeo very clearly."

The role sounds like a favourite. "Oh yes, and it's different every time. But I think it's going to be more special this time than any other." London audiences heard her sing it for ENO in 2003, but only in concert format; since then, Connolly says, she has grown "more technically capable. I've done things that have opened up the high notes, and expanded my general strength as a singer. I can make the phrases go on a bit longer, I can dare to sing more quietly." Perhaps the most important experience was singing the colossal role of Dido in Berlioz's The Trojans at ENO in 2004. "Once you've got through Dido's Farewell, and not died at the end of it, you realise you can get through anything."

Connolly's route to such epic roles has not been entirely conventional. Her initial training at the Royal College of Music was as a pianist; she spent five years in the BBC Singers, and then very nearly gave up classical singing for jazz. She even had a meeting set up with Ronnie Scott. "But I wanted so badly to sing Ravel's Shéhérazade, and I could tell the elasticity in my voice was disintegrating. I was breaking down my classical voice. So I chickened out." Initially at least, the decision to follow a classical career looked like it might have been the wrong one. "I had five years of auditions, which were a disaster." What kept her going? "A fascination with why I wasn't getting the work, when people I respected were telling me I had such a lovely voice."

Once she had that ENO Xerxes under her belt, Connolly established her versatility with several memorable leading roles at the Coliseum, notably in Handel, but also in repertoire from Monteverdi to Mark-Anthony Turnage. And yet, although she is now in demand internationally, there is perhaps a sense that some other UK companies have been slow off the mark in recognising her potential. This is the first time Opera North has come up with a role meaty enough to showcase the Yorkshire-born singer. More surprisingly, she is probably the most distinguished UK singer who has yet to appear with the Royal Opera - she does not make her debut there until next spring, when she heads the cast of Purcell's Dido and Aeneas. Does she ever feel that there's an operatic establishment that she hasn't quite cracked yet? "Not an establishment as such, but rather, I'd say, there's an inner circle of artists within which the people with the big recording contracts are invited, and I am slightly outside that."

By the time she sings at Covent Garden, her Dido will be on disc. Not, however, courtesy of any of the companies offering big recording contracts: Connolly raised the funding for the recording herself, which makes it sound like a vanity project until you consider the quality of the forces she was able to persuade to join her. She brought the Orchestra of the Age of Enlightenment on board, gathered together a cast of A-list colleagues including Gerald Finley, Patricia Bardon and John Mark Ainsley, and persuaded the independent label Chandos to take the project on. The whole thing was recorded, with no conductor, over two days in June.

"There's been a serious musicological approach to it," says Connolly, explaining that the version recorded is the one she sang at La Scala in 2006, which incorporates some extra pieces by Purcell. "It was something that just needed to be done. I felt there was nobody else singing Dido this way. I love playing with the major and minor harmonies - not in a jazzy way, but to colour it."

Connolly is not new to the idea of funding a recording herself - Heroes and Heroines, her outstanding 2004 Handel arias disc, had a similar genesis, and she has at least one other major project in the pipeline. "I'm very happy to be working with independent labels. You get far more artistic control. However, it's quite humiliating to have to go and beg for money." Artists' agents can also be taken aback to hear Connolly asking to book their singers. "I rang up John Tomlinson's agent the other day to see when he was free, and the agent said, 'Why are you asking?' I said, 'It's because it's me who's fixing the recording!' But the minute the agents hear who else I've got on board, there's never any question - they pencil it in and say, 'Good for you!' If you want something done in the recording industry, you have to just get off your bum and do it."

• I Capuleti e i Montecchi opens at the Grand Theatre, Leeds, on October 21, then tours. Details: www.operanorth.co.uk. Sarah Connolly is in recital at the Indig02, London on November 30. Her new CD, Schumann: Songs of Love and Loss, is out now